No , west Bengal students are not eligible for the Karnataka Common Entrance Test. ( K CET). Only candidates residing in Karnataka can appear for K CET.
K CET eligiblity criteria 2020
Candidate should be indian. Candidate should have passed 10+2 or equivalent exam with Physics Chemistry and maths with minimum 50%. Also candidates waiting for results of qualifying exam 2020 are eligible.
NOTE- KARNATAKA OPEN UNIVERSITY ( KSOU) CANDIDATES ARE NOT ALLOWED.
You may refer following link.
A candidate having a domicile of Karnataka is eligible to apply for KCET. Other state candidates can not apply for KCET unless you fall in some certain categories. I will provide the link below, you can check the eligibility there. You can appear for COMEDK exam instead.